Reachability Analysis-Based Interval Estimation for Discrete-Time Takagi–Sugeno Fuzzy Systems
Shenghui Guo, Weijie Ren, Choon Ki Ahn, Chenglin Wen, Hak‐Keung Lam
Abstract
Considering disturbances, noise, and sensor faults, this article investigates interval estimation for discrete-time Takagi–Sugeno fuzzy systems. To obtain precise estimation results and attenuate disturbances and noise in the system simultaneously, we integrate robust observers based on the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$ H_{\infty }$</tex-math></inline-formula> technique and reachability analysis. Two novel observer gain computation methods are proposed for different purposes. The time-invariant method relaxes the original design conditions by transforming the parameterized linear matrix inequality (LMI) into a series of LMIs to increase computational speed, while the time-varying method employs the parameterized LMI directly and conducts calculation online. Furthermore, reachable set representations for error dynamics are formulated by making use of both time-invariant observer gain and time-varying observer gain. An inverted pendulum system simulation and a comparative numerical simulation are studied to illustrate the effectiveness and superiority of the developed methods.